Do "End the turn" effects create ability-objects in the exile zone?

(For clarity, I'm going to use "ability-object" for the type of object that is on the stack, and "ability" for the element of text attached to an object like a card or token.)

I pay 2 and sacrifice a [[Clue]] to activate its ability. This creates an ability-object with the text "{2}+Sacrifice this artifact: Draw a card" on top of the stack. (Or is the ability-object's text just "Draw a card"?)

Holding priority, I then cast [[Discontinuity]], which resolves. Discontinuity exiles all spells and abilities on the stack. When tokens get exiled, they stop existing (111.7, 704.5d). When ability-objects resolve on the stack, they stop existing (608.2k). But as far as I can tell, there's no specific rule that prevents an ability-object from existing in other zones.

• Does anything the ability-object successfully go to the exile zone?
• If it does, does it have an ability? (My understanding is ability-objects get created on the stack with "rules text" but no "abilities", but I don't know if 400.7 "no memory" messes with that.)
• If they do exist, is it possible for an ability-object outside the stack to have any impact on the game?